


Reasonable approximations

by Beleriandings



Series: Tales of Lake Mithrim [15]
Category: The Silmarillion and other histories of Middle-Earth - J. R. R. Tolkien
Genre: Friendship, Gen, Mathematics, sort of cross-cultural
Language: English
Status: Completed
Published: 2015-01-30
Updated: 2015-01-30
Packaged: 2018-03-09 15:44:37
Rating: General Audiences
Warnings: No Archive Warnings Apply
Chapters: 1
Words: 2,027
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/3255353
Author URL: https://archiveofourown.org/users/Beleriandings/pseuds/Beleriandings
Summary: <blockquote class="userstuff">
              <p>Not long before leaving Lake Mithrim to take up his seat at Himring Hill, Maedhros makes an acquaintance. Later, at the Mereth Aderthad, they meet again.</p>
            </blockquote>





	Reasonable approximations

**Author's Note:**

> I was challenged to elaborate on the first meeting between Maedhros and his future friend and councillor Galineth (my OC) as mentioned offhand in my story The Burning Sky. For anyone who hasn’t read it, Galineth appears in chapter 3. Not that it is in any way essential reading for this; all you need to know is that Galineth is the little sister of Elenniel (Elenniel is my OC lover/partner of Lalwen) and the two sisters are leaders of a band of refugees from a sacked Mithrim Sindarin village who swore fealty to Fingolfin for protection from the orcs.

Maitimo paced the room impatiently, waiting for his brothers. They had been due to come to visit him from the other side of the lake today, and to go over the plans for his return to their own camp; Maitimo knew, with the sinking feeling that comes when one must face a task one has long put off, that today would be the day he would have to tell them. Today would be the day that he would tell them that he planned to give the crown to their uncle, that they would be Dispossessed in truth, as well as in name…

“Everything alright, Maitimo? I thought you were with your brothers?”

He wheeled around. “Fin.” He relaxed, smiling at Findekáno who had appeared in the doorway. “I thought they might be with you, or that they might be arguing with your father. Have you not seen them, then?”

Findekáno frowned. “No, I have not. I suppose they’re probably just late. Still…”

“Knowing them, they’ve probably gone and started something in your father’s camp. Come on, let’s go see if we can find them and keep them out of trouble.”

Findekáno grimaced, looping his arm through Maitimo’s. “Or at least stop them from causing any major diplomatic incidents.”

When they entered the main camp yard, the two of them suddenly found themselves faced with a somewhat surreal scene.

The girl was small and brown skinned, just barely scraping adulthood, with a head of wiry, wild silver curls and a frown on her face. She sat on an upturned bucket in the courtyard, flanked by her two unlikely companions, similarly seated. Even sitting, they both towered over her.

“I still think” said the girl in Sindarin, with the accent of the people of Mithrim, “that it makes not a blind bit of difference whether the – what do you call them? –  _infinitesimals_  mean anything in and of themselves, so long as the system  _works_. We can calculate things. Surely that’s what we want?” She folded her arms, raising a silvery eyebrow at the brothers.

Curufinwë gave a long-suffering sigh. “Your approach is refreshingly…  _applied_. But let me ask you this. What if we were to find that the whole system is flawed? We can define it formally, but as long as we do not understand - ”

“But we  _do_  understand” put in Carnistir, pointing at the piece of paper that lay between them, on another upturned bucket. “Approximately, the system is sound. We understand in terms of the equations. She’s right; we can use them to make meaningful predictions about the world, when precison is not of paramount importance. We can - ”

“Yes, but we haven’t even rigorously defined what we  _mean_  by infinitesimal” snapped Curufinwë. “ _Approaching infinitely close to zero_  is a decidedly vague and slippery concept. It’s like grasping a knife without knowing how long or sharp it is, or which end is pointing towards you.”

“Yes, but you used it to calculate the range for the catapult, just the other day” argued the Mithrim girl, stubbornly. “A ball of flaming pitch arced over the ridge and hit the orc camp in the next valley right in the middle, so I heard. We’d probably be crawling with orcs, otherwise.” She made a show of looking around her. “I don’t see any orcs. Do you?”

Carnistir looked amused. “She’s got you there, brother.”

Curufinwë frowned. “If you make an approximation when you are hurling burning pitch at orcs, that is one thing. But if you are trying to gain an understanding of the underlying principles that make it work…”

“Who is that?” asked Maedhros of Fingon, curiously.

A new voice came from behind them, and they both turned. “My little sister, regrettably.”

“Elenniel!” Maedhros inclined his head as Lalwendë and Elenniel came to join them, also arm in arm. “Forgive me, I had forgotten you even had a sister. What was her name, again…?”

“Galineth” said Elenniel, with a long-suffering sigh. Then she brightened. “She’s in her element with your brothers, though. I fear I was always too… well, not mathematically talented enough for her. She is frightfully clever, and a good education for her is one of the many benefits we have gained from joining ourselves to the host of Fingolfin.” She smiled, tilting her head to Lalwendë, who stood on tiptoe and kissed her affectionately on the cheek. “Though of course, not the only benefit.”

“You shouldn’t put yourself down so much” said Lalwendë to Elenniel, as Maitimo and Findekáno both smiled. “You’re clever. And I love you.”

“I love you too. But look!” said Elenniel, softening and leaning over to kiss Lalwendë. “Listen! They’re talking about the calculus again. I knew Curufinwë would regret lending Gali his book.”

“Approximations are  _useful_  though” Galineth was insisting. “Surely you can see that. And while you’re in the midst of the somewhat protracted process of formalising and proving all this, you’ll forgive us if your brother and I are putting what mathematical structure we _have_  to good, practical use.”

“The mathematics” Curufinwë was saying, somewhat loftily, “is beautiful for its own sake, I believe. But that’s not the point. You will thank me when my work results in your approximations using shaky notation and based on unformalised… well, glorified  _hunches,_ really… becoming useful, consistent and logically watertight methods.”

Galineth and Carnistir both rolled their eyes. Suddenly Carnistir caught sight of Maitimo. “Brother!” He exclaimed, still in Sindarin, his eyes lighting up at the sight of the little group of onlookers. “We were just about to go and find you.”

Maitimo raised an eyebrow. “No, no, don’t let me disturb anything” he said, laughing. “You’ve clearly got more important reasons to cross the lake than to merely see me.”

“It’s my fault” said Galineth contritely, although she was grinning. “We were having a most enjoyable discussion, weren’t we my lords?”

Curufinwë ground his teeth.

Maitimo felt that, all things considered, today might not be the best day to speak to him of the abdication. “Galineth” he said instead, bowing slightly. “I don’t believe we’ve met yet.”

She stretched out her left hand to clasp arms with him, not missing a beat. “I don’t believe we have. A pleasure, Lord Maedhros.”

“You are a mathematician?”

She blushed. “Well, when you put it like that it does sound very grand. I am… shall we say… an amateur. And a follower of your brother’s work. From a distance.”

“A lake’s span of distance” said Elenniel hastily, as Curufinwë made to form a biting remark.

Maitimo gave them all a smile, drawing up another bucket and sitting down on it as Findekáno, Lalwendë and Elenniel watched. “Will the three of you please explain what you were speaking of?” He arched an eyebrow. “I suppose I have been away from the intellectual life of our people for too long. But it sounds absolutely fascinating.”

“My pleasure” said Curufinwë, Carnistir and Galineth, all at once.

———-

The Mereth Aderthad, so far, had been a resounding success, and at long last Maedhros was content to sit beneath a tree outside the glow of firelight and watch Findekáno and Elenniel spin tirelessly across the dance floor. Macalaurë, predictably, had vanished, and Lalwendë was laughing with Aikanáro and a couple of Nandorin hunters in a grove or trees not far off.

He leaned back against the trunk sleepily, stretching out his long legs in front of him.

Unfortunately, someone was there to trip over them.

“Galineth!” Maitimo caught her by the sleeve and kept her from stumbling to the ground as she let out an impressive string of curses. “It’s been so long! I almost did not recognise you!”

For a moment, it seemed, in the dim light, that she did not recognise him. Then she grinned and flopped down beside him, pulling him into a tight hug. “Maedhros! How’s the east? Your brother sent me the latest draft of his treatise on derivatives and integrals, but I’ve seen neither hide nor hair of any of the sons of Fëanor apart form that. Fascinating stuff though. Very elegant mathematics. I find myself quite converted to his notation, embarrassingly enough. Actually, there were some points that I wanted to ask him about, and I was disappointed to find him not here with you.”

Maitimo smiled faintly. “Collectively, we thought it best that only my brother Maglor and I come to this gathering.”

She raised her hands before her. “Alright. Fair enough, I suppose. I did mean to travel to them, you know, on that last eastward trip your Finno… sorry, prince  _Fingon_ … took to see you. But I was needed at Barad Eithel.”

“Has my uncle set you to work then?”

“On the trade council, yes. Elenniel and Lalwen cooked up a position for me, and I have to thank them for the thought, at least. It’s better than being a scribe, I suppose. There’s a wonderful library there. Cannot complain, and all.”

He raised an eyebrow. “That doesn’t sound like the answer of someone who is content.”

She frowned for a moment. Then a wicked gleam appeared in her eye. “You won’t tell your uncle? Or my sister?”

Maedhros was nonplussed. “Not if you don’t want me to.”

“Promise?”

“Promise.”

“Oh thank Eru. Well, the truth is, Barad Eithel and my life there bores me senseless. Too many courtiers in ridiculous clothes, too much bickering dressed up in fancy words. You Golodhrim are good at that.”

He had to laugh. “Well, perhaps we are.” He was curious now. “What would you rather be doing then? Geometry? Writing books?”

“Oh, goodness me no!” She laughed. “Those are just some of my hobbies.” Her eyes turned a little misty. “No, I would love to be negotiating with someone. Working out clever deals. Diplomacy. Blatant arguing. All that. Did you know, I helped to make trade deals with the northern Mithrim villages that still stand, to bring all this food down for the feast? The fabric for the pavilions, too, although if you ask me, Duinel the councillor got a terrible deal there. Lucky it’s not raining now, because the stuff lets in water, and it was a  _criminal_ waste of all our surplus leather and furs from last year. Not that there was much. And to top it all off, the deal was done with a damned lot of fuss and bluster. I could have done it with less, and gotten a better deal, I’ll wager.”

He blinked. “You have an odd set of interests, has anyone ever told you that, Galineth?”

“How so? All I want is a nice simple place, free of court trappings, a place to read and to write and perhaps study a bit of mathematics on the side… ideally where I can easily correspond with your brother and borrow his books, the roads from here to the east are awful, did you know? You should get going on solving that problem!” She laughed at his expression. “I joke, I joke. I know you have the incentive of seeing your sweet Finno to motivate you as far as transport networks are concerned, and he has a similar idea. But anyway. All I want is a place to be able to do all that, write a little geometry and astronomy of my own, and maybe argue a few people into submission once in a while. Is that so much to ask?”

Maedhros was staring at her. “No” he said, on an impulse. “No, it’s really not. Galineth, I think I know just the place for you.”

“Really? Do enlighten me, lord.” She made a mocking bow, though she was sitting on the ground.

His mouth quirked upward in an amused smile. “How well do you like tall, cold hills on the edge of the world…?”

She smiled too, slowly. “Well, I suppose we shall find out. I daresay the High King can spare me.”

Maedhros smiled. “Good. Then I think I have a job for you, should you want it, on Himring hill. We can even fix the road situation, in time.”

“Good” said Galineth, shaking his hand once more. “I shall want to see my sister every so often.”


End file.
